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| Preface | |
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| List of Symbols | |
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| Introduction | |
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| Objectives of the study of structural dynamics | |
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| Importance of vibration analysis | |
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| Nature of exciting forces | |
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| Mathematical modeling of dynamic systems | |
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| Systems of units | |
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| Organization of the text | |
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| Formulation of the Equations of Motion: Single-Degree-of-Freedom Systems | |
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| Introduction | |
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| Inertia forces | |
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| Resultants of inertia forces on a rigid body | |
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| Spring forces | |
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| Damping forces | |
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| Principle of virtual displacement | |
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| Formulation of the equations of motion | |
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| Modeling of multi-degree-of-freedom discrete parameter system | |
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| Effect of gravity load | |
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| Axial force effect | |
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| Effect of support motion | |
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| Formulation of the Equations of Motion: Multi-Degree-of-Freedom Systems | |
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| Introduction | |
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| Principal forces in multi-degree-of-freedom dynamic system | |
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| Formulation of the equations of motion | |
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| Transformation of coordinates | |
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| Finite element method | |
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| Finite element formulation of the flexural vibrations of a beam | |
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| Static condensation of stiffness matrix | |
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| Application of the Ritz method to discrete systems | |
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| Principles of Analytical Mechanics | |
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| Introduction | |
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| Generalized coordinates | |
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| Constraints | |
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| Virtual work | |
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| Generalized forces | |
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| Conservative forces and potential energy | |
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| Work function | |
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| Lagrangian multipliers | |
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| Virtual work equation for dynamical systems | |
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| Hamilton's equation | |
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| Lagrange's equation | |
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| Constraint conditions and lagrangian multipliers | |
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| Lagrange's equations for discrete multi-degree-of-freedom systems | |
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| Rayleigh's dissipation function | |
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| Free Vibration Response: Single-Degree-of-Freedom System | |
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| Introduction | |
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| Undamped free vibration | |
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| Free vibrations with viscous damping | |
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| Damped free vibration with hysteretic damping | |
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| Damped free vibration with Coulomb damping | |
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| Forced Harmonic Vibrations: Single-Degree-of-Freedom System | |
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| Introduction | |
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| Procedures for the solution of the forced vibration equation | |
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| Undamped harmonic vibration | |
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| Resonant response of an undamped system | |
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| Damped harmonic vibration | |
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| Complex frequency response | |
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| Resonant response of a damped system | |
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| Rotating unbalanced force | |
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| Transmitted motion due to support movement | |
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| Transmissibility and vibration isolation | |
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| Vibration measuring instruments | |
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| Energy dissipated in viscous damping | |
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| Hysteretic damping | |
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| Complex stiffness | |
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| Coulomb damping | |
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| Measurement of damping | |
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| Response to General Dynamic Loading and Transient Response | |
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| Introduction | |
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| Response to an impulsive force | |
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| Response to general dynamic loading | |
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| REsponse to a step function load | |
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| Response to a ramp function load | |
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| Response to a step function load with rise time | |
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| Response to shock loading | |
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| Response to ground motion | |
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| Analysis of response by the phase plane diagram | |
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| Analysis of Single-Degree-of-Freedom Systems: Approximate and Numerical Methods | |
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| Introduction | |
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| Conservation of energy | |
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| Application of Rayleigh method to multi-degree-of-freedom systems | |
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| Improved Rayleigh method | |
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| Selection of an appropriate vibration shape | |
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| Systems with distributed mass and stiffness: Analysis of internal forces | |
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| Numerical evaluation of Duhamel's integral | |
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| Direct integration of the equations of motion | |
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| Integration based on piece-wise linear representation of the excitation | |
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| Derivation of general formulae | |
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| Constant-acceleration method | |
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| Newmark's [beta] method | |
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| Wilson-[theta] method | |
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| Methods based on difference expressions | |
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| Errors involved in numerical integration | |
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| Stability of the integration method | |
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| Selection of a numerical integration method | |
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| Selection of time step | |
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| Analysis of nonlinear response | |
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| Errors involved in numerical integration of nonlinear systems | |
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| Analysis of Response in the Frequency Domain | |
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| Transform methods of analysis | |
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| Fourier series representation of a periodic function | |
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| Response to a periodically applied load | |
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| Exponential form of fourier series | |
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| Complex frequency response function | |
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| Fourier integral representation of a nonperiodic load | |
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| Response to a nonperiodic load | |
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| Convolution integral and convolution theorem | |
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| Discrete Fourier transform | |
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| Discrete convolution and discrete convolution theorem | |
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| Comparison of continuous and discrete Fourier transforms | |
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| Application of discrete inverse transform | |
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| Comparison between continuous and discrete convolution | |
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| Discrete convolution of an infinite- and a finite-duration waveform | |
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| Corrective response superposition methods | |
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| Exponential window method | |
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| The fast Fourier transform | |
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| Theoretical background to fast Fourier transform | |
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| Computing speed of FFT convolution | |
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| Free-Vibration Response: Multi-Degree-of-Freedom Systems | |
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| Introduction | |
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| Standard eigenvalue problem | |
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| Linearized eigenvalue problem and its properties | |
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| Expansion theorem | |
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| Rayleigh quotient | |
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| Solution of the undamped free-vibration problem | |
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| Mode superposition analysis of free-vibration response | |
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| Solution of the damped free-vibration problem | |
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| Additional orthogonality conditions | |
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| Damping orthogonality | |
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| Numerical Solution of the Eigenproblem | |
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| Introduction | |
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| Properties of standard eigenvalues and eigenvectors | |
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| Transformation of a linearized eigenvalue problem to the standard form | |
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| Transformation methods | |
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| Iteration methods | |
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| Determinant search method | |
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| Numerical solution of complex eigenvalue problem | |
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| Semi-definite or unrestrained systems | |
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| Selection of a method for the determination of eigenvalues | |
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| Forced Dynamic Response: Multi-Degree-of-Freedom Systems | |
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| Introduction | |
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| Normal coordinate transformation | |
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| Summary of mode superposition method | |
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| Complex frequency response | |
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| Vibration absorbers | |
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| Effect of support excitation | |
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| Forced vibration of unrestrained system | |
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| Analysis of Multi-Degree-of-Freedom Systems: Approximate and Numerical Methods | |
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| Introduction | |
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| Rayleigh-Ritz method | |
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| Application of Ritz method to forced vibration response | |
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| Direct integration of the equations of motion | |
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| Analysis in the frequency domain | |
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| Analysis of nonlinear response | |
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| Formulation of the Equations of Motion: Continuous Systems | |
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| Introduction | |
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| Transverse vibrations of a beam | |
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| Transverse vibrations of a beam: variational formulation | |
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| Effect of damping resistance on transverse vibrations of a beam | |
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| Effect of shear deformation and rotatory inertia on the flexural vibrations of a beam | |
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| Axial vibrations of a bar | |
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| Torsional vibrations of a bar | |
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| Transverse vibrations of a string | |
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| Transverse vibrations of a shear beam | |
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| Transverse vibrations of a beam excited by support motion | |
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| Effect of axial force on transverse vibrations of a beam | |
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| Continuous Systems: Free Vibration Response | |
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| Introduction | |
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| Eigenvalue problem for the transverse vibrations of a beam | |
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| General eigenvalue problem for a continuous system | |
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| Expansion theorem | |
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| Frequencies and mode shapes for lateral vibrations of a beam | |
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| Effect of shear deformation and rotatory inertia on the frequencies of flexural vibrations | |
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| Frequencies and mode shapes for the axial vibrations of a bar | |
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| Frequencies and mode shapes for the transverse vibration of a string | |
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| Boundary conditions containing the eigenvalue | |
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| Free-vibration response of a continuous system | |
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| Undamped free transverse vibrations of a beam | |
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| Damped free transverse vibrations of a beam | |
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| Continuous Systems: Forced-Vibration Response | |
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| Introduction | |
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| Normal coordinate transformation: general case of an undamped system | |
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| Forced lateral vibration of a beam | |
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| Transverse vibrations of a beam under traveling load | |
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| Forced axial vibrations of a uniform bar | |
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| Normal coordinate transformation, damped case | |
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| Wave Propagation Analysis | |
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| Introduction | |
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| The phenomenon of wave propagation | |
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| Harmonic waves | |
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| One-dimensional wave equation and its solution | |
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| Propagation of waves in systems of finite extent | |
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| Reflection and refraction of waves at a discontinuity in the system properties | |
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| Characteristics of the wave equation | |
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| Wave dispersion | |
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| Answers to Selected Problems | |
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| Index | |